Pure Exploration and Regret Minimization in Matching Bandits

TL;DR

This paper introduces a novel approach to the matching bandits problem, leveraging a rank-1 assumption to significantly improve sample complexity and regret bounds, advancing the efficiency of algorithms in combinatorial matching tasks.

Contribution

It demonstrates how a rank-1 assumption on the adjacency matrix can reduce sample complexity and regret in matching bandits, a novel theoretical contribution.

Findings

Reduced sample complexity with rank-1 assumption

Lower regret bounds for matching bandits

Improved efficiency of algorithms in combinatorial matching

Abstract

Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1 assumption on the adjacency matrix to reduce the sample complexity and the regret of off-the-shelf algorithms up to reaching a linear dependency in the number of vertices (up to poly log terms).